The extrusion of plasticized material mixtures into cellular structures (i.e., honeycomb) requires a delicate balance of deformability (for shape molding) and structural integrity (for shape retention). Such mixtures can include inorganic ceramic powders, a binder component and a liquid component, the amounts of which are controlled to maintain low pressure, torque, and temperature during the extrusion process while creating a self-supporting body which is able to be handled upon formation. The cellular structure of the extrudate can be formed such that cells near the periphery of the formed body can have a smaller or reduced cross-section compared to cells near the middle or center of the body. In an ideal or pristine cellular structure, pressure equilibrium is achieved between the internal pressure of each cell and the ambient or atmospheric pressure outside the body.